ashok borrowed rupees 12000 at some rate percent compound interest . after a year he paid back rupees 4000.if compound interest for the second year be rupees 920 find :
i. the rate of interest charged
ii. the amount of debt at the end of the Second year
pls answer with correct steps
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8th
Maths
Comparing Quantities
Compound Interest
Ashok borrowed Rs. 12,000 a...
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Asked on December 26, 2019 by
Simeen Dan
Ashok borrowed Rs. 12,000 at some rate percent compound interest. After a year, he paid back Rs. 4,000. If compound interest for the second year be Rs. 920, Find the rate of interest charged.
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ANSWER
Principle =Rs. 12,000
Let the rate of interest be x%
Amount to be paid after one year(A)
=P(1+
100
R
×t)
A=12,000(1+
100
x
×1)
=Rs.(12000+120x)
since, Rs. 4000 was paid back
Balance amount =12000+120x−4000
=Rs.(8,000+120x)
∴ Principal for 2
nd
year $$(P^1}=$$Rs. (8000+120x)
Amount to be paid after 2
nd
year =P
1
(1+
100
R
×t)
t=1 year
R=x%
P
1
=Rs.(8000+120x)
=(8000+120x)(1+
100
x
+1)
=1.2x
2
+200x+8000
Compound interest for 2
nd
year =Rs.920
=Amount at the end of 2
nd
year − principle for 2
nd
year
∴1:2x
2
+200x+8000−(8000+120x)=920
∴1.2x
2
+80x−920=0
∴x=
2×1.2
−80±
80
2
−4×(−920)×1.2
∴ Since rate of interest cannot be negative
x=
2.4
−80+
80
2
+4×920×1.2
x=
2.4
−80=104
∴x=10
∴ Rate of interest =10%.
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Answer:
Rs. 10,120
Explainatoin:
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